Embodiments according to the invention relate to a micromechanical element and a method for producing a micromechanical element.
A series of different micromirrors are known. For example, micromechanically produced mirrors for active focus variation bendable in a convex and/or concave manner are known. A very simplified illustration (cross-section) of a mirror deflectable according to the bimorph principle is shown, for example, in FIGS. 9a and 9b. Here, the mirror plate 900 consists of at least two layers 910 and 920 of different materials.
In order to be able to actively bend the mirror plate, a lateral mechanical expansion εx and εy has to be actively adjustable in at least one layer. The actively adjustable expansion can be generated, for example, with the help of thermal excitation (thermomechanical bimorph/for example with electrothermal heating), wherein the materials of both layers 910 and 920 have different coefficients of linear expansion, piezoelectric and electrostrictive excitation (electroactive monomorphs, bimorphs and multimorphs using the transversal effect) and piezomagnetic and magnetostrictive excitation (magnetoactive mono, bi and multimorphs using the transversal effect). In the cases of electroactive excitation via transversal effects in electroactive (piezoelectric and electrostrictive) solids, the mirror plate has to consist of at least three different layers (two electrodes and an electroactive layer arranged outside the line of zero expansion (“neutral fiber”).
An exemplary arrangement of an electroactive monomorph 1000 (frequently also referred to as unimorph) is shown in FIGS. 10a and 10b. Here, the electroactive layer 1020 is arranged between two electrode layers 1010 and 1030. If an electric voltage is applied between both electrode layers, an electric field Ez will be created within the electroactive layer. Due to the existence of the electric field and the transversal effects, a lateral expansion εx and εy will generated within the electroactive layer 1020. In the case of piezoelectric materials, this mechanical expansion depends directly, and in the case of electrostrictive materials in a square-law manner, on the electric field strength and results in a bending of the mirror plate 1000.
For further possible layer arrangements of such devices, for example, two active materials are used in bimorphs, or multiple layer stacks in multimorphs connected in parallel with the aim of reducing the necessitated electric drive voltage.
Generally, parabolic surface profiles (rotation paraboloides) are suitable for focusing light with the help of mirrors. If a plate is bent due to lateral expansion (by the above shown monomorph and bimorph arrangements), a spherical surface profile (hemisphere) results at “small” deflections. In “Conrad, H., Klose, T., Sander, T., Schenk, H., Lakner, H.: Actuating Methods of Quasistatic Micromirrors for Active Focus Variation. Proc. of the IEEE 2008 International Students and Young Scientists Workshop “Photonics and Microsystems”, pp. 7-11, 2008” it has been shown based on simple calculations, that depending on the lateral dimensions (diameter) of the mirror plate, the deviation between spherical and parabolic surface profile is negligibly small up to a focus length of approximately 3 cm. Hence, spherically bent mirror plates are also suitable for focusing light.
Further mircomirrors exist for active focus variation, which are deflected with the help of the electrostatic drive principle (e.g., “Shao, Y., Dickensheets, D.-L., Himmer, P.: 3-D MOEMS Mirror for Laser Beam Pointing and Focus Control. IEEE Journal of Selected Topics in Quantum Electronics, Vol. 10, No. 3, pp. 528-535, 2004” and “Mescheder, U. M., Estan, C., Somogyi, G. Freudenreich, M.: Distortion optimized focusing mirror device with large aperture. Sensors and Actuators A, 130-131, pp. 20-27, 2006”). Compared to the bimorph and monomorph deflectable mirrors, micromirrors necessitate higher electric drive voltages (“Conrad, H., Klose, T., Sander, T., Schenk, H., Lakner, H.: Actuating Methods of Quasistatic Micromirrors for Active Focus Variation. Proc. of the IEEE 2008 International Students and Young Scientists Workshop “Photonics and Microsystems”, pp. 7-11, 20”). In these micromirrors, the curvature variation is caused by a force (of the electrostatic field) vertically active at the mirror plate. Such electrostatically driven systems are to be distinguished from electrostatically actively bendable systems as mentioned above.
Generally, due to technological limitations in the production of such a micro system (release of the mirror plate) and for better resistance against mechanical environmental influences (shock resistance), the mirror plate can be connected at its edge to a fixed frame via spring elements. FIG. 11 shows an example of such a micromirror 1100 (black: open, etched trenches). Here, this actively bendable mirror plate 1110 is fixed at the frame 1130 of the device 1100 via four spring elements 1132.
This results in deformation errors by restoring forces of the suspension of the mirror plate 1110. The spring elements 1132 are designed such that they counteract the movement of edges 1112 and 1114 of the mirror plate with mechanical restoring forces that are as small as possible. Here, the spring elements are strained both with regard to bending and torsion. For the mirror plate to be able to bend due to the actively coupled lateral expansion, the edge of the mirror plate has to be freely moving to the greatest possible extent.
The edge of the mirror plate moves laterally (the mirror plate contracts or expands) and the edge of the mirror plate is tilted.
Since the mirror plate is connected to the fixed frame 1130 at discrete attachment positions 1112 at the plate edge via spring elements 1132, and the spring elements cannot be implemented infinitely soft (due to the shock resistance and manufacturability of the device), the mirror plate experiences less spherical bending in the direction of the attachment position 1112 and more spherical bending in the direction of the free plate edge 1114.
Hence, a non-rotation symmetrical deformation profile results in the circular mirror plate 1110. The deviation (error) to the spherical or parabolic deformation profile is positive in the direction of the free plate edge and negative in the direction of the spring elements. The amount of deviation from the ideal deformation profile depends on the lateral size of the mirror plate (e.g. diameter d in a circular plate), occurs already at small deflections and results in a significant decrease of the optical quality of the focusing mirror.
Additionally, non-linear deformation errors in large deflections can occur. The above-mentioned purely spherical deformation profile caused by lateral expansion of a layer within a plate applies only for “small” deflections. The deflection is small when the bending w is smaller than the whole plate thickness t (w and t see FIG. 9). For larger deflections, the linear plate theory (so-called Kirchhoff's Plate Theory) does no longer apply. The higher the ratio of bending to the overall plate thickness (w/t), the more the plate assumes diaphragm-like behavior, which is characterized by little to no bending strength. This results in “fold-like” surface profiles or fold-like deviations from the ideal deformation profile. These fold-like deviations from the ideal deformation profile occur within the whole mirror plate and result in a significant decrease of the optical quality at large deflections (curvatures) of the focus mirror.
Theoretically, it would be possible to minimize this non-linear error by a thick mirror plate (t is higher than the bending w maximally necessitated for the target application). However, producing thick mirror plates with the help of microsystem technology is very expensive (reason: depositing and structuring of thick layers) and the bending moment to be overcome is non-linearly dependent on the plate thickness (bending moment˜plate thickness3), significantly higher driving forces in the form of higher actively coupled lateral expansions (which have to be generated by higher electric voltages, for example in the case of electroactive functional layers) are necessitated for bending thick plates.